It is understood that Juventus would ideally love to pair Van Persie and Suarez in a dream attack.
Whether either deal is pushed on remains to be seen, but Italian champions Juve are aiming big.
They have already made a firm move for Van Persie but, as with rival bidders Manchester City and Manchester United, have not been able to agree terms with Arsenal.
Sky Sports understands that Arsenal are standing firm over their valuation of the Dutch striker, who confirmed earlier this summer he did not wish to extend his contract, which has one year left.
Whilst Juve continue to work on a possible deal for Van Persie, they also have an interest in Suarez.
But it is understood that their interest in Suarez is long-standing and their ideal scenario was to sign both players but whether either deal can be done remains to be seen.
Despite his troubles last season, Suarez remains popular with the Anfield faithful and his performances underlined his quality.
Indeed Liverpool are hoping to agree a new deal with Suarez, who returned to pre-season training on Tuesday.